Model Predictive Control Basics

Model predictive control (MPC) is a feedback methodology where a finite-horizon optimal control problem (OCP) is solved iteratively. The OCP uses a system model to find the best control sequence over a set period by minimizing a cost function while adhering to system dynamics and constraints. This tutorial provides a hands-on guide to coding an MPC controller in Python using the CasADi library for a simple linear system known as the double integrator. The implementation involves defining the OCP with its cost and constraints, solving it to find an open-loop control sequence, and then repeatedly re-solving with updated state measurements to create a closed-loop feedback system.